This paper is focused on the structure of the order parameter variations between zero and the bulk values as a result of the MF screening by the Meissner currents, and therefore the phenomenology used here takes the view on mesoscopic rather than macroscopic (hydrodynamic) scales, while information on the hydrodynamic excitations is lost.
Indeed, the GL model for terrestrial SCs works well only for mesoscopic length scales and does not describe the hydrodynamic excitations.
Both the GL theory and the zero-temperature hydrodynamics are based on the notion of the wave function, but can be equivalently formulated in terms of the SF densities and velocities.
This duality is a convenient feature for application to various types of problems, for the wave function description is in fact a mechanical description in terms of densities and momenta as opposed to description in terms of densities and velocities.
Recently, it has been explicitly shown in detail [1]},[2]} that treatment for the SF hydrodynamics in terms of fluid momenta [3]} is equivalent to treatment in terms of velocities [4]},[5]}.
